Question
Asked Dec 25, 2019
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A series RLC circuit has resistance R = 12.0 Ω, inductive reactance
XL = 30.0 Ω, and capacitive reactance XC = 20.0 Ω. If
the maximum voltage across the resistor is  ΔVR= 145 V, find
the maximum voltage across (a) the inductor and (b) the
capacitor. (c) What is the maximum current in the circuit?
(d) What is the circuit’s impedance?

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Expert Answer

Step 1

Part A:

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GivenInfo: The resistance of the resistor is 12.0 N. The inductive reactance is XL = 30.0 N. The capacitive reactance is Xc = 20.0 N. The maximum voltage across the resistor is 145 V. The maximum current through the circuit in terms of the resistance is give by, AVR,max (1) Imax AVR,max is the maximum voltage across the resistor Ris the resistance

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Step 2
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The maximum current through the circuit in terms of the inductive reactance is give by, AVL,max (2) XI. Imax AVLmax is the maximum voltage across the inductor Xị is the inductive reactance From (1) and (2), AVR,max AVL,max mах R X1,

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Step 3
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On re-arrangement for the maximum voltage across the inductor, XLAVR,max AVL,max = The resistance of the resistor is 12.0 2. The inductive reactance is XL = 30.0 2. The capacitive reactance is Xc = 20.0 N. The maximum %3D voltage across the resistor is 145 V. Substitute 12.0N for R, 30.0 N for XL, 145 V for AVR.max determine the maximum voltage across the inductor, (30.02)(145 V) AVL,max 12.02 = 363 V Conclusion: The maximum voltage across the inductor is 363 V.

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